As such, the herein described Impermanent Loss dynamics also apply to UniswapV3 pools.Įxisting studies show that reducing tick sizes may be beneficial in creating fair conditions for both market makers and market takers and promote high frequency trade, however it may also lead to an increase in queue undercutting behaviors if the change leads to an increase in tick spreads. We finally focus on the UniswapV3 protocol, which introduced the notion of concentrated liquidity ranges and show that such a position can be replicated by leveraging a classic UniswapV2 pool while simultaneously hedging part of the underlying token price exposition. This suggests that G3M pools are not yet efficiently arbitraged as agents may access ex-ante knowledge of which G3M pools are likely to be far better investment proposals than others. The cross-sectional dispersion of ROI has however been high and the pool net ROI ranking has been significantly autocorrelated for several weeks. It appears that the median liquidity pool had a net nil ROI when taking Impermanent Losses into account. We then turn to empirical data to establish if transaction fee income has historically been high enough to offset Impermanent Losses and allow G3M investments to outperform their continually rebalanced constant-mix portfolio counterparts. We establish non-arbitrage bounds for the wealth process of such Automated Market Makers in the presence of transaction fees and highlight the dynamic of their so-called Impermanent Losses, which are incurred due to negative convexity and essentially void the benefits of portfolio diversification within G3Ms. Geometric Mean Market Makers (G3M) such as Uniswap, Sushiswap or Balancer are key building blocks of the nascent Decentralised Finance system. We study numerically the form of the incentives and their impact on the shape of the order book, and analyze the sensitivity of the incentives to the market parameters. Moreover, when studying the asymptotic behavior of the solution, a specific penalty function enables the exchange to obtain closed-form incentives at each limit of the order book. Due to the particular nature of the SPDE control problem, we are able to characterize the solution with a classic Feynman-Kac representation theorem. We formulate the control problem of the exchange who wishes to modify the shape of the order book by increasing the volume at specific limits. The incentives proposed to the market participants are functions of the time and the distance of their limit order to the mid-price. We model the limit order book as the solution of a stochastic partial differential equation (SPDE) as in. In this paper, we study the problem of an exchange using incentives in order to increase market liquidity.
Consequently, they developed several regulatory tools to control liquidity provision / consumption on their liquidity pool. With the fragmentation of electronic markets, exchanges are now competing in order to attract trading activity on their platform. This representationallows identifying each market participant’s influence over the price covariance. Under the framework of multivariate Hawkes processes,we express the covariance of price as a consequence of cascading order flows arriving on the LOB. The lastpart of this thesis highlights the analysis of price covariance. We also proposed a more reliable GMM estimator to calibrate the Hurst parameter H. Our approach unifies two famousvolatility models, the rough fractional stochastic volatility (RFSV) model and the multifractal random walk (MRW), underthe same framework. Fromthe Gaussian random field, we construct a family of parametrized random processes. The second part is dedicated to the analysis of rough volatility. Ergodicity is proven in this model,which allows one to apply it for simulation purposes. In our model, the intensity of order flows dependsexplicitly on the current state of the Limit Order Book and also on past order flows.
We combine multivariate Hawkes processeswith the so-called “queue reactive" property firstly introduced in. We start byconstructing an order flows model under the framework of point processes. This thesis is dedicated to the study of market microstructure and price dynamics in the electronic market.
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